论文标题
紧凑的Kähler歧管具有缓慢动态的自动形态
Automorphisms of compact Kähler manifolds with slow dynamics
论文作者
论文摘要
我们研究紧凑型Kähler歧管具有缓慢动力学的自动形态。通过调整格罗莫夫的古典论点，我们在多项式熵上给出了上限，并在尺寸上研究其可能的值$ 2 $和$ 3 $。我们证明，具有均方根衍生物生长的每种自动形态都是等轴测图。在$ c^{\ infty} $上下文中给出了反示例，在多项式熵上对Artigue，Carrasco-Olivera和Monteverde进行负回答。最后，我们将最小的自动形态分类为尺寸$ 2 $，并证明它们仅存在于Tori上。我们猜想对于任何维度都是正确的。
We study the automorphisms of compact Kähler manifolds having slow dynamics. By adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that every automorphism with sublinear derivative growth is an isometry ; a counter-example is given in the $C^{\infty}$ context, answering negatively a question of Artigue, Carrasco-Olivera and Monteverde on polynomial entropy. Finally, we classify minimal automorphisms in dimension $2$ and prove they exist only on tori. We conjecture that this is true for any dimension.
